Reservoir properties are sampled at well logs (wireline, LWD or cased-hole logs). Proper characterization of a reservoir, particularly for estimates of net rock volume, porosity volume, and original oil in place, requires an estimate of the property distributions of shale volume, porosity, saturation, etc. and the uncertainty of these property distributions. Property distribution uncertainty is a key component of reservoir characterization that affects volumetric uncertainty and reservoir recovery forecasts.
Methods for predicting reservoir properties such as porosity and the shale percentage in a 3D volume from seismic attributes and inversion products have been described in the literature and are widely available from vendors such as Hampson-Russell, Jason Geophysical, or Rock Solid. However, these tools generally suffer from two limitations. A first limitation is that the empirical calibration of the seismic properties to the observed reservoir properties inherently creates an unrealistic reservoir property histogram. For example, FIG. 1 depicts an example of a probability distribution function (PDF) using a conventional method of a field porosity predicted from seismic attributes. As shown in FIG. 1, the PDF obtained using the conventional seismic-porosity method shows negative porosities which is clearly a defect of the conventional method. A second limitation is that the uncertainty of the predicted values in the volume and/or the predicted property histogram is not quantitatively accounted for.
These limitations need to be addressed because quantitative oil in place (OIP) assessment is based on an accurate prediction of field-wide reservoir property histogram, percentage of the histogram above an economic cutoff which may lie at an extremity of the distribution, and the uncertainty of these statistics. For example, the EMERGE product of Hampson-Russell of CGGVeritas which predicts reservoir properties using seismic attributes and well log data, uses step-wise linear regression and Gaussian distribution fitting for seismic-well calibration. Both of these processes, i.e., step-wise linear regression and Gaussian distribution fitting, by their very mathematical nature tend to produce predicted reservoir property histograms that do not capture the shape or extremes of the distribution. FIG. 2 depicts a comparison between a probability distribution function (PDF) of a field porosity obtained by conventional step-wise linear regression and a probability distribution function (PDF) of a field porosity obtained from well data. As shown in FIG. 2, the PDF obtained using the conventional regression method under-represents the porosity below 0.05 or above 0.25 when compared with the porosity obtained from well data.
Geostatistical sequential Gaussian property simulation methods require as input a property histogram to be used to derive the backward and forward transform cumulative distribution function (see, Deutsch, C. V. and A. G. Journel, GSLIB: Geostatistical Software Library and User's Guide, 2nd Ed. New York: Oxford University Press 1998). This requirement can lead geostatistical practitioners to use the property histogram of the hard-data, which is most often a property data at the well locations at which the model will be fitted exactly, as the external histogram constraint. However, the use of hard-data defeats the purpose of using soft-data. Soft-data most often is based on seismic attributes that capture property variations between well control in a modeling process.
One way of addressing this issue was proposed by Deutsch et al. (see, Deutsch, C. V., P. Frykman, and Y. L. Xie, Declustering with Seismic or “soft” Geologic Data, Centre for Computational Geostatistics Report One 1998/1999, University of Alberta). Deutch et al. proposed to decluster the histogram using soft-data which is also known as soft-data debiasing. The process described can be used when there is a good statistical correlation between the hard-data and soft-data (see, Vejbæk, O. V., and L. Kristensen, 2000, Downflank hydrocarbon potential identified using seismic inversion and geostatistics: Upper Maastrichtian reservoir unit, Dan Field, Danish Central Graben: Petroleum Geoscience, v. 6, p. 1-13). Unfortunately, statistical correlation between the hard-data and soft-data does not occur when all of the hard-data and soft-data are examined in one set. As a result, conventional methods do not provide a satisfactory answer.
Therefore, there is a need for a system and a method of using spatially independent subsets of data to determine the uncertainty of soft-data debiasing of property distributions for spatially correlated reservoir data.